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A Surprising Link Between Math and Business

Game theory is a study of strategic decision making. This mathematical theory was developed in the 1950s. It looked at how interactive decision making between two competitors will impact the eventual outcome. Game theory is used extensively in many fields such as games, politics, economics and even biology.

But interestingly, we are also able to catch a glimpse of how game theory works in the realm of business.

Basics of Game Theory

There are many examples used to explain game theory. Perhaps the most famous of them is the prisoner’s dilemma. The example goes like this:

1) Two criminals get caught

2) Each is taken to a separate negotiating room with no chance of communicating with each other

3) Each is given a choice of confessing to their crime or denying it

4) However, each criminal is also informed that if he denies and his partner confesses, he would go to jail for 15 years while his partner would walk free

5) If they both deny, they would both go to jail for a year

6) If they both confess, they would both go to jail for 5 years

Under such circumstances, the outcomes that both criminals face can be mapped by the following diagram:

Years in Prison for both criminals (Prisoner 1/Prisoner 2) Prisoner 2 confesses Prisoner 2 denies
Prisoner 1 confesses 5 / 5 0 / 15
Prisoner 1 denies 15 / 0 1 / 1

Without being able to communicate with the other party, the most logical decision for both of them is to deny the charges and spend just a year in prison rather than risk spending the next 15 years holed up in a cell.

Can it Work in Business?

As we have established, like in the above, cooperating with your competitors might actually be the most logical decision rather than slugging it out in an attempt to eliminate other parties.

In Singapore, the telecommunication sector could be one where companies could use game theory to weigh their decisions.

The local market is dominated by Singtel (SGX: Z74), Starhub (SGX: CC3) and M1 (SGX: B2F). To simplify the example, we can look at the decision making process if we only take into account the management of Singtel and Starhub. Every year, both managements might choose to raise prices or reduce prices. Given that there are implications to each decision, a hypothetical payoff table might look like this:

Revenue Gain
(Singtel / Starhub)
Starhub raise prices Starhub reduce prices
SingTel raise prices 5% / 5% -10% / 0%
SingTel reduce prices 0% / -10% -5% / -5%

If both reduce prices, nothing will happen to their market share and they both face a drop in their revenue. If however, Singtel decides to raise prices but Starhub reduces its prices, Singtel might lose some customers to Starhub, resulting in a drop of 10% in revenue. Starhub on the other hand will not enjoy a rise in revenue as the increase in customer base is offset by the reduction in prices. From the table, it seems that the most reasonable action for both managements to take is to raise prices together, resulting in a gain in revenue for both parties.

Foolish Summary

The reason why using game theory to make a decision is different from price collusion is because each side is making a decision without knowledge of what the other party is going to do. Although the SingTel and Starhub example can be too simplistic, it  serves to bring home a very important point: Sometimes in business the most logical decision is not to destroy your competition, but rather to match each other in strategy to ensure the survival and prosperity of both companies.

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The information provided is for general information purposes only and is not intended to be personalised investment or financial advice. Motley Fool Singapore contributor Stanley Lim doesn’t own shares in any companies mentioned.